82 research outputs found
Features of gravitational waves in higher dimensions
There are several fundamental differences between four-dimensional and
higher-dimensional gravitational waves, namely in the so called braneworld
set-up. One of them is their asymptotic behavior within the Cauchy problem.
This study is connected with the so called Hadamard problem, which aims at the
question of Huygens principle validity. We investigate the effect of braneworld
scenarios on the character of propagation of gravitational waves on FRW
background.Comment: to appear in ERE09 proceeding
Geometrical classification of Killing tensors on bidimensional flat manifolds
Valence two Killing tensors in the Euclidean and Minkowski planes are
classified under the action of the group which preserves the type of the
corresponding Killing web. The classification is based on an analysis of the
system of determining partial differential equations for the group invariants
and is entirely algebraic. The approach allows to classify both characteristic
and non characteristic Killing tensors.Comment: 27 pages, 20 figures, pictures format changed to .eps, typos
correcte
Covariants,joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature
The invariant theory of Killing tensors (ITKT) is extended by introducing the
new concepts of covariants and joint invariants of (product) vector spaces of
Killing tensors defined in pseudo-Riemannian spaces of constant curvature. The
covariants are employed to solve the problem of classification of the
orthogonal coordinate webs generated by non-trivial Killing tensors of valence
two defined in the Euclidean and Minkowski planes. Illustrative examples are
provided.Comment: 60 pages. to appear in J. Math. Phy
Killing spinor space-times and constant-eigenvalue Killing tensors
A class of Petrov type D Killing spinor space-times is presented, having the
peculiar property that their conformal representants can only admit Killing
tensors with constant eigenvalues.Comment: 11 pages, submitted to CQ
Equivalence problem for the orthogonal webs on the sphere
We solve the equivalence problem for the orthogonally separable webs on the
three-sphere under the action of the isometry group. This continues a classical
project initiated by Olevsky in which he solved the corresponding canonical
forms problem. The solution to the equivalence problem together with the
results by Olevsky forms a complete solution to the problem of orthogonal
separation of variables to the Hamilton-Jacobi equation defined on the
three-sphere via orthogonal separation of variables. It is based on invariant
properties of the characteristic Killing two-tensors in addition to properties
of the corresponding algebraic curvature tensor and the associated Ricci
tensor. The result is illustrated by a non-trivial application to a natural
Hamiltonian defined on the three-sphere.Comment: 32 page
Relativistic GPS in 3-dimensions
We extend to three dimensions the proposal of a completely relativistic
positioning system (rPS). The system does not rely on approximations, in fact,
it works at a few Schwarzschild radii from a black hole, and it does not rely
on Newtonian physics or special relativity. Since general relativity (GR)
claims to be our fundamental framework to describe classical physics, it must
provide tools to bootstrap physics within the theory itself, without relying on
previous approximated frameworks. The rPS is able to self-diagnose, that is, it
detects deviations from assumptions about the gravitational field and
consequently stops operations; in addition it is robust, i.e., it is able to
autonomously restore operations when assumptions are restored. From a more
general viewpoint, the rPS is equivalent to geodesy in spacetime, which
establishes a (conventional) coordinate system on a surface by means of
measurements within the surface itself, as well as allowing it to extract
information about the intrinsic geometry of the same surface. In other words,
the positioning system is potentially able to extract information about the
gravitational field (which in fact is identified with the geometry of
spacetime) in addition to the gravitational theory, which describes its
dynamics. Thus, it becomes a framework within which one can operationally
distinguish different theories of gravitation.Comment: 29 pages, 8 figure
Two special classes of space-times admitting a non-null valence two Killing spinor
Non-conformally flat space-times admitting a non-null Killing spinor of
valence two are investigated in the Geroch-Held-Penrose formalism. Contrary to
popular belief these space-times are not all explicitly known. It is shown that
the standard construction hinges on the tacit assumption that certain
integrability conditions hold, implying two algebraic relations, KS1 and KS2,
for the spin coefficients and the components of the Ricci spinor. An exhaustive
list of (conformal classes of) space-times, in which either KS1 or KS2 are
violated, is presented. The resulting space-times are each other's Sachs
transforms, in general admit no Killing vectors and are characterized by a
single arbitrary function.Comment: 12 pages; typos corrected, complex transfo added, references adde
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